In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the traditional category of individual, it supplies an adequate meta-language to speak of the proposed ontology of properties and its structure.

We present a generalization of the problem of pattern recognition to arbitrary probabilistic models. This version deals with the problem of recognizing an individual pattern among a family of different species or classes of objects which obey probabilistic laws which do not comply with Kolmogorov’s axioms. We show that such a scenario accommodates many important examples, and in particular, we provide a rigorous definition of the classical and the quantum pattern recognition problems, respectively. Our framework allows for the introduction of (...) non-trivial correlations between the different species involved, opening the door to a new way of harnessing these physical resources for solving pattern recognition problems. Finally, we present some examples and discuss the computational complexity of the quantum pattern recognition problem, showing that the most important quantum computation algorithms can be described as non-Kolmogorovian pattern recognition problems. (shrink)

We discuss the mathematical structures that underlie quantum probabilities. More specifically, we explore possible connections between logic, geometry and probability theory. We propose an interpretation that generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories. We stress the relevance of developing a geometrical interpretation of quantum mechanics.

En este artículo, analizamos el significado de las matrices densidad en el formalismo de la mecánica cuántica. Discutimos el problema de los "sistemas cuánticos compuestos" en la lógica cuántica así como también la interpretación de las mezclas impropias. Tomando en cuenta el desarrollo de la lógica cuántica convexa, presentamos un análisis de la estructura formal de la teoría que, argumentaremos, debe ser considerado a la hora de desarrollar un nuevo esquema conceptual para la interpretación de las mezclas cuánticas. In this (...) article, we analyze the meaning of density matrices within the formalism of quantum mechanics. We discuss the problem of compound systems in the context of quantum logic as well as the interpretation of improper mixtures. Taking into account the development of convex quantum logic, we present an analysis of the formal structure of the theory which we will argue, must be taken into account when developing a new conceptual scheme for the interpretation of quantum mixtures. (shrink)

In this work, we focus on the philosophical aspects and technical challenges that underlie the axiomatization of the non-Kolmogorovian probability framework, in connection with the problem of quantum contextuality. This fundamental feature of quantum theory has received a lot of attention recently, given that it might be connected to the speed-up of quantum computers—a phenomenon that is not fully understood. Although this problem has been extensively studied in the physics community, there are still many philosophical questions that should be properly (...) formulated. We analyzed different problems from a conceptual standpoint using the non-Kolmogorovian probability approach as a technical tool. (shrink)

It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of (...) solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions. (shrink)

We study the origin of quantum probabilities as arising from non-Boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorovian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case).

Mereology deals with the study of the relations between wholes and parts. In this work we will discuss different developments and open problems related to the formulation of a quantum mereology. In particular, we will discuss different advances in the development of formal systems aimed to describe the whole-parts relationship in the context of quantum theory.

We discuss the relationship between logic, geometry and probability theory under the light of a novel approach to quantum probabilities which generalizes the method developed by R. T. Cox to the quantum logical approach to physical theories.

We discuss generalized pobabilistic models for which states not necessarily obey Kolmogorov's axioms of probability. We study the relationship between properties and probabilistic measures in this setting, and explore some possible interpretations of these measures.

In this work we discuss logical structures related to indistinguishable particles. Most of the framework used to develop these structures was presented in [17, 28] and in [20, 14, 15, 16]. We use these structures and constructions to discuss possible ontologies for identical particles. In other words, we use these structures in order to characterize the logical structure of quantum systems for the case of indistinguishable particles, and draw possible philosophical implications. We also review some proposals available in the literature (...) which may be considered within the framework of the quantum logical tradition regarding the problem of indistinguishability. Besides these discussions and constructions, we advance novel technical results, namely, a lattice theoretical structure for identical particles for the finite dimensional case. This kind of approach was not present in the scarcely literature of quantum logic and indistinguishable particles. (shrink)

This paper introduces the theory QST of quasets as a formal basis for the Nmatrices. The main aim is to construct a system of Nmatrices by substituting standard sets by quasets. Since QST is a conservative extension of ZFA (the Zermelo-Fraenkel set theory with Atoms), it is possible to obtain generalized Nmatrices (Q-Nmatrices). Since the original formulation of QST is not completely adequate for the developments we advance here, some possible amendments to the theory are also considered. One of the (...) most interesting traits of such an extension is the existence of complementary quasets which admit elements with undetermined membership. Such elements can be interpreted as quantum systems in superposed states. We also present a relationship of QST with the theory of Rough Sets RST, which grants the existence of models for SQT formed by rough sets. Some consequences of the given formalism for the relation of logical consequence are also analysed. (shrink)

Despite of its formal precision and its great many applications, Shannon’s theory still offers an active terrain of debate when the interpretation of its main concepts is the task at issue. In this article we try to analyze certain points that still remain obscure or matter of discussion, and whose elucidation contribute to the assessment of the different interpretative proposals about the concept of information. In particular, we argue for a pluralist position, according to which the different views about information (...) are no longer rival, but different interpretations of a single formal concept. (shrink)

Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build (...) a vector space with inner product, the Q-space, using the non-classical part of quasi-set theory, to deal with indistinguishable elements. Vectors in Q-space refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the fact of unobservability of permutations. Thus, this paper can be regarded as a tentative to follow and enlarge Heinsenberg’s suggestion that new phenomena require the formation of a new “closed” (that is, axiomatic) theory, coping also with the physical theory’s underlying logic and mathematics. (shrink)

The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schrödinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first-order language using quasiset theory (Q). In this work, we (...) show that Q cannot capture one of the most important features of quantum non-individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities, the quasicardinal needs not necessarily be a primitive concept. (shrink)

In this paper we discuss the notions of adequacy and truth functionality in quantum logic from the point of view of a non-deterministic semantics. We give a characterization of the degree of non-functionality which is compatible with the propositional structure of quantum theory, showing that having truth-functional connectives, together with some assumptions regarding the relation of logical consequence, commits us to the adequacy of the interpretation sets of these connectives. An advantage of our proof is that it is independent of (...) the number of truth values involved, generalizing previous works. We also show the failure of the adequacy of every Nmatrix that is a model of the non-distributive lattice of quantum propositions. En este trabajo discutimos las nociones de adecuación y veritativo-funcionalidad en la lógica cuántica, desde el punto de vista de una semántica no determinista. Damos una caracterización del grado de no-funcionalidad compatible con la estructura proposicional de la teoría cuántica, mostrando que tener conectivos veritativo-funcionales, junto con algunos presupuestos relativos a la relación de consecuencia lógica, nos compromete con la adecuación de los conjuntos de interpretación de estos conectivos. Un punto ventajoso de nuestra prueba es que se independiza de la cantidad de valores de verdad involucrados, generalizando trabajos previos. Probamos también que falla la adecuación de cualquier Nmatriz que sirva como modelo para el retículo no distributivo de proposiciones cuánticas. (shrink)

Quantum indistinguishability directly relates to the philosophical debate on the notions of identity and individuality. They are crucial for our understanding of multipartite quantum systems. Furthermore, the correct interpretation of this feature of quantum theory has implications that transcend fundamental science and philosophy, given that quantum indistinguishability is a resource in quantum information theory. Most of the conceptual analysis of quantum indistinguishability is restricted to studying the permutational invariance of quantum states, the concomitant quantum statistics and their entanglement. Here, we (...) analyse the role of indistinguishability and non-individuality in other areas of quantum theory. We start by analysing how a very peculiar use of indistinguishability underlies Feynman’s rules for summing amplitudes in interference phenomena. Next, we study how quantum indistinguishability is underestimated in several topics of debate in the quantum physics literature, such as the Einstein–Podolsky–Rosen argument, Bell’s inequalities and the Bell–Kochen–Specker theorem. Finally, we argue that an ontology of truly indistinguishable entities can serve as a basis for a quantum ontology that can give interesting answers to the interpretational problems of quantum mechanics. We claim that, in addition to superposition, contextuality and entanglement, indistinguishability (understood in a robust ontological sense) is one of the central features of quantum physics. -/- . (shrink)

In the present paper we develop different arguments to show that there are no reasons to consider that there exists quantum information as qualitatively different than Shannon information. There is only one kind of information, which can be coded by means of orthogonal or non-orthogonal states. The analogy between Shannon’s theory and Schumacher’s theory is confined to coding theorems. The attempt to extend the analogy beyond this original scope leads to a concept of quantum information that becomes indistinguishable from that (...) of quantum state. But information is essentially linked with communication, as it is clear in both Shannon’s and Schumacher’s proposals. If we detach information from this link, we are not talking about information but about quantum mechanics. We also stress the neutrality of information with respect to the physical theories that describe the systems used for its implementation. This view opens the way towards a non-reductive unification of physics: if different physical theories can be reconstructed on the same neutral informational basis, they could be meaningfully compared with no need of searching for reductive links among them. (shrink)

Can there be two things that are completely indistinguishable? This simple question has raised numerous debates throughout the history of philosophy and science. The principle of the identity of indiscernibles claims that no two things can be completely indiscernible. But this thesis has been challenged in quantum physics and continues to be a hot topic in cutting edge areas of mathematics. The question has gained a renewed interest with the possibility of harnessing indistinguishability as a resource in quantum information tasks. (...) This theme issue is devoted to understanding identity and indistinguishability in philosophy and science, gathering an interdisciplinary group of experts in the field. It will allow readers of diverse disciplines to have an updated introduction to the topic. (shrink)

Combining physics and philosophy, this is a uniquely interdisciplinary examination of quantum information science. Suitable as both a discussion of the conceptual and philosophical problems of this field and a comprehensive stand-alone introduction, this book will benefit both experienced and new researchers in quantum information and the philosophy of physics.

In this work, we discuss a formal way of dealing with the properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This framework allows us to consider a new ontology (...) in order to study the properties of quantum systems. (shrink)

It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default, sheaf theory, topos theory, and non-standard or signed probabilities. In this paper we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum particles or properties (...) can be indistinguishable yet different, no contradiction arising from a Kochen-Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same. We will discuss how the consequences of this move may help us understand quantum contextuality. (shrink)

In this work we present a dynamical approach to quantum logics. By changing the standard formalism of quantum mechanics to allow non-Hermitian operators as generators of time evolution, we address the question of how can logics evolve in time. In this way, we describe formally how a non-Boolean algebra may become a Boolean one under certain conditions. We present some simple models which illustrate this transition and develop a new quantum logical formalism based in complex spectral resolutions, a notion that (...) we introduce in order to cope with the temporal aspect of the logical structure of quantum theory. (shrink)

The more common scheme to explain the classical limit of quantum mechanics includes decoherence, which removes from the state the interference terms classically inadmissible since embodying non-Booleanity. In this work we consider the classical limit from a logical viewpoint, as a quantum-to-Boolean transition. The aim is to open the door to a new study based on dynamical logics, that is, logics that change over time. In particular, we appeal to the notion of hybrid logics to describe semiclassical systems. Moreover, we (...) consider systems with many characteristic decoherence times, whose sublattices of properties become distributive at different times. (shrink)

It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of (...) solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions. (shrink)

Plato's political thought gave rise to a number of concepts and issues - such as the idea of a normative theory, the philosophical foundation of politics, the philosopher-kings, the standard of utopian theory - which have played a significant role on Western political and philosophical thought. -/- This volume aspires to bring out Plato's concept of efficacy in a normative theory. -/- By efficacy, the author means the way in which the theory conceives of its practical realization. If in the (...) Republic this issue is particularly problematic, in the Laws, instead, the claim of realizability becomes the main concern. -/- By defining the concept of efficacy and going through the main works of Plato, this conceptual and textual analysis aims to shed a new light on Plato's political thought, which is neither a utopia, nor a short term political program, but the first normative theory encompassing a theory of efficacy. (shrink)

Intuitively, we can conceive of the existence of a conscious state as a pure activity that does not necessarily require a body (or even a brain). This idea has found new support in certain recent theories that present the possibility of a totally disconnected and disembodied consciousness. Against this hypothesis, I argue that human experience is intrinsically embodied and embedded, though in a specific way. Using Sartre’s phenomenology of the body, I first analyze the concept of consciousness as intentionality and (...) a world-disclosing activity, thus explaining how conscious activity can only be expressed through a body that is spatiotemporally related to the world. Then, I argue that bodily consciousness does not necessarily imply the actual presence of an anatomical body but, rather, a process of spatialization and temporalization (hodological space and temporal synthesis) through the “spatiotemporal body”. Finally, I test my thesis by critiquing some cases of apparent disembodied/disconnected consciousness, i.e., dreams, out-of-body experiences, and the brain-in-a-vat scenario. (shrink)

According to the received view in epistemology, inferential knowledge from non-knowledge is impossible – that is, in order for a subject to know the conclusion of their inference, they must know the essential premises from which that conclusion is drawn. In this book, Federico Luzzi critically examines this view, arguing that it is less plausible than intuition suggests and that it can be abandoned without substantial cost. In a discussion that ranges across inference, testimony and memory he analyses the (...) full range of challenges to the view, connecting them to epistemological cases that support those challenges. He then proposes a defeater-based framework which allows the phenomenon of knowledge from non-knowledge across these three epistemic areas to be better understood. His book will be of interest to a wide range of readers in epistemology. (shrink)

While some form of loss of control is often assumed to be a common feature of the diverse manifestations of addiction, it is far from clear how loss of control should be understood. In this paper, I put forward a concept of decrease in control in addiction that aims to fill this gap and thus provide a general framework for thinking about addictive behavior. The development of this account involves two main steps. First, I present a view of degrees of (...) control as the degree to which an agent would be responsive to potential or counterfactual sufficient reasons to do otherwise. Second, I sketch an account of the relevant control-undermining factors in addiction that is consonant with my proposed view of degrees of control. Being a high-level functional property, reasons-responsiveness is particularly well suited to frame an account of control-undermining factors that is doubly pluralistic: it encompasses the contribution of factors both internal and external to the agent, and it is consistent with various proposals as to the precise nature of the anomaly taking place in the psychology of addiction. (shrink)

Human cerebral organoids are three-dimensional biological cultures grown in the laboratory to mimic as closely as possible the cellular composition, structure, and function of the corresponding organ, the brain. For now, cerebral organoids lack blood vessels and other characteristics of the human brain, but are also capable of having coordinated electrical activity. They have been usefully employed for the study of several diseases and the development of the nervous system in unprecedented ways. Research on human cerebral organoids is proceeding at (...) a very fast pace and their complexity is bound to improve. This raises the question of whether cerebral organoids will also be able to develop the unique feature of the human brain, consciousness. If this is the case, some ethical issues would arise. In this article, we discuss the necessary neural correlates and constraints for the emergence of consciousness according to some of the most debated neuroscientific theories. Based on this, we consider what the moral status of a potentially conscious brain organoid might be, in light of ethical and ontological arguments. We conclude by proposing a precautionary principle and some leads for further investigation. In particular, we consider the outcomes of some very recent experiments as entities of a potential new kind. (shrink)

A restrictive view of self-control identifies exercises of self-control with synchronic intrapsychic processes, and pictures diachronic and externally-scaffolded strategies not as proper instances of self-control, but as clever ways of avoiding the need to exercise that ability. In turn, defenders of an inclusive view of self-control typically argue that we should construe self-control as more than effortful inhibition, and that, on grounds of functional equivalence, all these diverse strategies might be properly described as instances of self-control. In this paper, I (...) take a fresh look at this debate by focusing on cases of addiction. I argue that addicted agents face a paradigmatic sort of self-control challenge, which makes addiction an important test case for theories of self-control. And I discuss evidence that highlights both the unreliability of synchronic intrapsychic strategies and the crucial role that is played by diachronic and externally-scaffolded strategies in successful attempts at achieving abstinence by addicted individuals. Abstaining addicts are a paradigmatic case of agents who successfully exercise self-control, and they mostly do so by relying on diachronic and externally-scaffolded strategies. This, I argue, lends further support to an inclusive view of self-control. (shrink)

According to a shared functionalist view in philosophy of mind, a cognitive system, and cognitive function thereof, is based on the components of the organism it is realized by which, indeed, play a causal role in regulating our cognitive processes. This led philosophers to suggest also that, thus, cognition could be seen as an extended process, whose vehicle can extend not only outside the brain but also beyond bodily boundaries, on different kinds of devices. This is what we call the (...) ‘Externally Extended Cognition Thesis.’ This notion has generated a lively debate. Here, we offer a novel notion of extended cognition, according to which cognition can be seen as being realized outside the brain, but still inside the body. This is what we call the ‘Internally Extended Cognition Thesis’. Not only our thesis but also our approach while defending it is innovative. The argument we offer is supported by recent empirical findings in the life sciences and biomedicine, which suggest that the gut microbiota’s activity has a functional role in regulating our cognitive processes and behaviors. In doing so, we embrace the holobiont-perspective, according to which it is possible to claim that what we call biological individuals are not autonomous entities with clear boundaries, but should rather be seen as networks of multiple interactions among species. Thus, by analyzing different sets of evidence in light of the holobiont-perspective, we argue that the gut microbiota could be seen as a component of our organism. On the basis of the philosophical interpretation of this evidence, however, we also suggest that there are no impediments standing the way of considering the gut microbiota also as a functional extension of our cognitive system. If so, this amounts to extending cognition out of ‘our skull’, though still confining it within ‘our body’: to ‘our gut’. This is an instance of the ‘Internally Extended Cognition Thesis,’ whose benefits for an original theory of extended cognition are discussed. (shrink)

The social sciences are predominantly seen by their practitioners as critical endeavours, which should inform criticism of harmful institutions, beliefs and practices. Accordingly, political attacks on the social sciences are often interpreted as revealing an unwillingness to accept criticism and an acquiescence with the status quo. But this dominant view of the political implications of social scientific knowledge misses the fact that people can also be outraged by what they see as its apologetic potential, namely that it provides excuses or (...) justifications for people doing bad things, preventing them from being rightfully blamed and punished. This introduction to the special issue sketches the long history of debates about the exculpatory and justificatory consequences of social science and lays the foundations for a theory of social scientific apologia by examining three main aspects: what social and cognitive processes motivate this type of accusation, how social theorists respond to it and whether different contexts of circulation of ideas affect how these controversies unfold. (shrink)

We will present a three-valued consequence relation for metainferences, called CM, defined through ST and TS, two well known substructural consequence relations for inferences. While ST recovers every classically valid inference, it invalidates some classically valid metainferences. While CM works as ST at the inferential level, it also recovers every classically valid metainference. Moreover, CM can be safely expanded with a transparent truth predicate. Nevertheless, CM cannot recapture every classically valid meta-metainference. We will afterwards develop a hierarchy of consequence relations (...) CMn for metainferences of level n. Each CMn recovers every metainference of level n or less, and can be nontrivially expanded with a transparent truth predicate, but cannot recapture every classically valid metainferences of higher levels. Finally, we will present a logic CMω, based on the hierarchy of logics CMn, that is fully classical, in the sense that every classically valid metainference of any level is valid in it. Moreover, CMω can be nontrivially expanded with a transparent truth predicate. (shrink)

En su más reciente libro, Cuestiones de Filosofía del Lenguaje: Pragmática, David Pérez Chico (2022) nos presenta una muy interesante selección de artículos sobre diferentes temáticas actualmente trabajadas en filosofía del lenguaje. Personalmente, considero que este libro es una lectura imprescindible para cualquier lector de habla hispana que quiera introducirse en las temáticas más contemporáneamente discutidas en esa disciplina. En este marco, en el presente artículo me propongo realizar un análisis crítico de cuatro de los artículos de la compilación que (...) trabajan la temática de las emisiones evaluativas, i.e., emisiones cuya extensión depende de parámetros contextuales semánticamente no estándares. (shrink)

Following the proposal of a new kind of selective structural realism that uses as a basis the distinction between framework and interaction theories, this work discusses relevant applications in fundamental physics. An ontology for the different entities and properties of well-known theories is thus consistently built. The case of classical field theories—including general relativity as a classical theory of gravitation—is examined in detail, as well as the implications of the classification scheme for issues of realism in quantum mechanics. These applications (...) also shed light on the different range of applicability of the ontic and epistemic versions of structural realism. (shrink)

Este trabajo tematiza la cuestión de los programas informáticos que discriminan, desde la filosofía del lenguaje. En esta disciplina, la bibliografía sobre discurso de odio ha centrado su análisis en los efectos que este produce en los grupos oprimidos. La idea central del presente trabajo será presentar una nueva noción, el discurso influenciado, que permita explicar lo que el grupo opresor es llevado a afirmar en base a la opresión sistemática. Así, el discurso influenciado permitirá tanto explicar la reproducción social (...) de los discursos de odio como enmarcar teóricamente las afirmaciones discriminatorias realizadas por los programas informáticos previamente mencionados. (shrink)